But David Lewis is a materialist and determinist who believes that our world, the actual world, could not have been otherwise. Thus, Lewis is not a true possibilist. He insists that all his possible worlds are real and actual (cf. Hegel's "the real is the actual"). In each of Lewis's possible worlds, there are no possibilities other than the completely determined actualities. All of David Lewis's possible worlds are actual worlds!

There are no real possibilities in any of David Lewis's possible worlds. For information philosophy, possibilities are of course not real in the sense of actual, but are realized when they are actualized. Possibilities have the same existential or ontological status as ideas, especially multiple ideas in a mind that are evaluated as .alternative possibilities for action.

Possible worlds and modal reasoning made "counterfactual" arguments extremely popular in current philosophy. Possible worlds, especially the idea of "nearby worlds" that differ only slightly from the actual world, are used to examine the validity of modal notions such as necessity and contingency, possibility and impossibility, truth and falsity.

But counterfactuals and Lewis's counterpart theory are just language games, ways of talking, that analytic language philosophers and metaphysicians have found productive. They do have an ontological commitment to possibilities or ideas.

Lewis appears to have believed that the truth of his counterfactuals was a result of believing that for every non-contradictory statement there is a possible world in which that statement is true.

True propositions are those that are true in the actual world.

False propositions are those that are false in the actual world.

Necessarily true propositions are those that are true in all possible worlds.

Contingent propositions are those that are true in some possible worlds and false in others.

Possible propositions are those that are true in at least one possible world.

Impossible propositions are those that are true in no possible world .

Compatibilism says that our choices are free insofar as they manifest our
characters (our beliefs, desires, etc.) and are not determined via causal
chains that bypass our characters. If so, freedom is compatible with
predetermination of our choices via our characters. The best argument for
compatibilism is that we know better that we are sometimes free than that we
ever escape predetermination; wherefore it may be for all we know that we are
free but predetermined.

Incompatibilism says that our choices are free only if
they have no determining causes outside our characters - not even causes that
determine our choices via our characters. The best argument for incompatibilism
rests on a plausible principle that unfreedom is closed under implication.

Consider the prefix 'it is true that, and such-and-such agent never had any
choice about whether', abbreviated 'Unfree'; suppose we have some premises (zero
or more) that imply a conclusion; prefix 'Unfree' to each premise and to the
conclusion; then the closure principle says that the prefixed premises imply the
prefixed conclusion. Given determinism, apply closure to the implication that
takes us from preconditions outside character - long ago, perhaps - and
deterministic laws of nature to the predetermined choice. Conclude that the
choice is unfree. Compatibilists must reject the closure principle. Let's assume
that incompatibilists accept it. Else why are they incompatibilists?
I'll speak of compatibilist freedom' and 'incompatibilist freedom'. But I don't
ask you to presuppose that these are two varieties of freedom. According to
incompatibilism, compatibilist freedom is no more freedom than counterfeit money
is money.

It seems that free-will theodicy must presuppose incompatibilism. God could
determine our choices via our characters, thereby preventing evil-doing while
leaving our compatibilist freedom intact. Thus He could create utopia, a world
where free creatures never do evil.

Plantinga once responded to compatibilist opponents as if their objection were a
terminological quibble. The hypothesis is that God permits evil so that our
actions may be not determined. If you find 'free' a tendentious word, use
another word: 'unfettered', say. But of course the issue is one of value, not
terminology. The opponents grant the value of compatibilist freedom. But they
think that if God permits evil for the sake of incompatibilist freedom, what He
gains is worthless.

There are no real possibilities in any of David Lewis's possible worlds.

Yet for purposes of mere 'defence' it needn't be true, or even plausible, that
incompatibilist freedom has value. It is enough that it be possible. Plantinga's
short way with the compatibilists would have been fair if, but only if, it was
common ground that a false and implausible value judgement is nevertheless
possible.

Before we turn back to the free-will theodicy that does presuppose
incompatibilism, let's consider the compatibilist alternative a little further.
Suppose God did determine our choices via our characters, preventing evil-doing
while leaving us free.

Lewis is a materialist and determinist who believes the world is causally closed under the laws of nature.

How might He do it? By a wise choice of initial
conditions and uniform, powerful, simple laws of nature? - That might be
mathematically impossible. The problem might be overconstrained. It might be
like the problem: find a curve which is given by an equation no more than
fifteen characters long, and which passes through none of the following hundred
listed regions of the plane.

Many philosophers criticize the idea of "gaps" in the laws of nature, some equating it with ontological chance

Rather, God might attain utopia by elaborate contrivance; Instead of uniform and
powerful laws of nature, He could leave the laws gappy, leaving Him room to
intervene directly in the lives of His creatures and guide them constantly back
to the right path. Or (if indeed this is possible) His laws might be full of
special quirks designed to apply only to very special cases. Either way, despite
our compatibilist freedom, God would be managing our lives in great detail,
making extensive use of His knowledge and power.

In a 1981 article in Theoria, David Lewis said that van Inwagen's Consequence Argument fails as a reductio ad absurdum argument. Van Inwagen agreed and called Lewis' article “the finest essay that has ever been written in defense of compatibilism – possibly the finest essay that has ever been written about any aspect of the free will problem”. ("How to Think about the Problem of Free Will”, Journal of Ethics (2008) 12, 337-341).

Kadri Vihvelin has written a critical analysis of van Inwagen and Lewis's reply. She says "The Consequence Argument was supposed to show that if we attribute ordinary abilities to deterministic agents, we are forced to credit them with incredible past or law-changing abilities as well. But no such incredible conclusion follows. All that follows is something that we must accept anyway, as the price of our non-godlike nature, that humans have "finite minds," so that the exercise of our abilities depends partly on circumstances outside our control.

Temporal Parts

Besides his extravagant and outlandish (literally!) invention of infinite possible worlds, Lewis also exploded our actual world into an infinity of "temporal parts," with properties he calls "temporary intrinsics."

In his analysis of the metaphysical problem of the persistence of objects, the question of their identity over time, Lewis proposes the idea of temporal parts. He calls his solution "perdurance," which he distinguishes from "endurance," which he says is different from ordinary persistence, but this difference is not made clear.

Lewis says:

Our question of overlap of worlds parallels the this-worldly problem of
identity through time; and our problem of accidental intrinsics parallels
a problem of temporary intrinsics, which is the traditional problem of
change. Let us say that something persists iff, somehow or other, it
exists at various times; this is the neutral word.

The road parts do not exactly persist. They are intrinsically different parts. The enduring entity does persist simpliciter. There is zero evidence of a discontinuous process that produces a disappearance and reappearance. It would violate physical conservation laws

Something perdures iff
it persists by having different temporal parts, or stages, at different times.
though no one part of it is wholly present at more than one time; whereas
it endures iff it persists by being wholly present at more than one time.
Perdurance corresponds to the way a road persists through space; part
of it is here and part of it is there, and no part is wholly present at two
different places. Endurance corresponds to the way a universal, if there
are such things, would be wholly present wherever and whenever it is
instantiated. Endurance involves overlap: the content of two different
times has the enduring thing as a common part. Perdurance does not.

(On the Plurality of Worlds, p. 202)

This is a variation of an Academic Skeptic argument about growth, that even the smallest material change destroys an entity and another entity appears. There is no physical or metaphysical reason for this wild assumption. Nevertheless, Lewis's "counterfactual" thinking is highly popular among modern metaphysicians. .